Let $h(x)=x^{^{\scriptsize\dfrac{5}{2}}}$. $h'(x)=$
The derivative of $h$ can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) $\begin{aligned} &\phantom{=}h'(x) \\\\ &=\dfrac{d}{dx}\left(x^{^{\frac{5}{2}}}\right) \\\\ &=\dfrac{5}{2}x^{^{\frac{5}{2}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac52x^{^{\frac{3}{2}}} \end{aligned}$ In conclusion, we found that $h'(x)=\dfrac52x^{^{\frac{3}{2}}}$. This can also be written as $2.5\sqrt{x^3}$ (all equivalent forms are accepted).